Generalized Bi-Quasi-Variational Inequalities for Quasi-Pseudo-Monotone Type II Operators in Non-Compact Settings

Abstract

A new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II operators in non-compact settings has been introduced in locally convex Hausdorff topological vector spaces. Some existence results of solutions for the above  GBQVI have been obtained.
In 1985, K.C. Border \cite{2} introduced the concept of escaping sequences in the book: "Fixed Point Theorems with Applications to Economics and Game Theory".

Using this concept of escaping sequences, we shall obtain our results on GBQVI for quasi-pseudo-monotone type II operators in non-compact settings. But the main tools that we shall apply in obtaining our results are  Chowdhury and Tan's result on generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets.

As application, an existence theorem on generalized bi-complementarity problem for quasi-pseudo-monotone type II operators is given in non-compact settings